Understanding Class-D amplifier power supply requirements

Specifying the power supply requirements for audio amplifiers can be tricky. If the power supply is overdesigned it will add unnecessary cost to the product, and if it supply is underdesigned the amplifier will not meet its performance specifications. This article reviews the steps necessary to determine the power supply requirements for an audio amplifier.

There are several factors that a designer must consider when designing the power supply for an audio amplifier:

• Number of outputs and output voltage(s)
• Peak output current
• Average and peak output power
• Input voltage range for target geographic markets
• Line and load regulation
• Ripple and noise
• Size and weight
• Efficiency and standby power consumption requirements
• Safety, EMI, and other regulatory requirements
• Cost requirements

The factors listed above will determine the best type of power supply to use in any given application.

Power Supply Output Voltage and Current
The power supply voltage is one of the primary factors in determining how much power an amplifier can deliver to the load. The voltage required for an amplifier depends on several factors, including:

• the amplifier's output power requirements
• the load (speaker) impedance
• the amplifier output configuration (single-ended or BTL)
• the amplifier's maximum achievable duty cycle
• stray resistance in the output path

The nominal power supply output voltage is also a function of the power supply's output voltage tolerance and its line and load regulation. The amplifier should be able to provide its rated power at the minimum power supply output voltage, taking all of the above factors into account.

The maximum RMS power that an amplifier can deliver to the load without clipping is:

P_BTL(RMS) = [(V_CC • M_MAX)² / (2 • R_T²)] • R_LOAD

where R_T is the sum of all of the DC resistances in series with the load:

R_T = R_LOAD + R_OUT + R_IND + R_PCB + R_PS

where

R_LOAD is the load (speaker) resistance,

R_OUT is the on-resistance (R_DSon) of the amplifier's output transistors (one transistor for single-ended outputs and two transistors for BTL outputs),

R_IND is the DC resistance of the output filter inductors,

R_PCB the resistance of the circuit board traces, connectors, and wires, and

R_PS is the power supply output impedance.

Note that most of these resistances have temperature coefficients so it is important to use the component's resistance at its maximum operating temperature. This is particularly important for components that may have significant power dissipation such as the amplifier IC and the filter inductors.

M_MAX is the amplifier's maximum output duty cycle. Duty cycle is also referred to as the modulation index (M), and M_MAX is the maximum modulation factor.

Because amplifiers with BTL outputs can provide twice the peak-to-peak voltage to the load as a single-ended amplifier, the maximum output power of a single-ended amplifier is only ¼ of the maximum output power of a BTL amplifier with the same power supply voltages and load impedance.

P_SE(RMS) = [(V_CC/2 • M_MAX)² / (2 • R_T²)] • R_LOAD

                 = [(V_CC • M_MAX)² / (8 • R_T²)] • R_LOAD

                 = ¼ • [((V_CC • M_MAX)² / (2 • R_T²)) • R_LOAD]

                 = ¼ P_BTL(RMS)

The peak output power occurs at the peak of the voltage or current into the speaker. The peak power that an amplifier can deliver to the load is

P_BTL(PEAK) = I_O²R_L = (V_O/R_T)² R_L = 2 • P_BTL(RMS) for amplifiers with BTL outputs

P_SE(PEAK) = I_O²R_L = (V_O/2R_T)² R_L = ¼(V_O/R_T)² R_L = 2 • P_SE(RMS) for amplifiers with single-end outputs

where V_O is the amplifier output voltage (speaker voltage) and I_O is the output current.